System and method for dynamic fast tobogganing

ABSTRACT

A method of identifying an object in a digital image includes finding a point in a digital image that is a concentration location, initializing a cluster with said concentration location, adding the neighboring points of the concentration location to a list, selecting a neighbor point with an extremal potential value from said list, determining a slide direction of all neighbors of said selected point and identifying those neighbors that slide to the selected point, adding those neighbor points not already in the list to the list, adding the selected point to the cluster, and repeating the steps of selecting a neighbor point with an extremal potential value, determining a slide direction, adding points to the list, and adding the selected point to the cluster, until the list is empty.

CROSS REFERENCE TO RELATED UNITED STATES APPLICATIONS

This application claims priority from “Dynamic Fast Toboggan”, U.S.Provisional Application No. 60/577,527 of Liang, et al., filed Jun. 7,2004, the contents of which are incorporated herein by reference.

TECHNICAL FIELD

This invention is directed to toboggan-based object segmentation indigital medical images.

DISCUSSION OF THE RELATED ART

The diagnostically superior information available from data acquiredfrom current imaging systems enables the detection of potential problemsat earlier and more treatable stages. Given the vast quantity ofdetailed data acquirable from imaging systems, various algorithms mustbe developed to efficiently and accurately process image data. With theaid of computers, advances in image processing are generally performedon digital or digitized images.

Digital images are created from an array of numerical valuesrepresenting a property (such as a grey scale value or magnetic fieldstrength) associable with an anatomical location points referenced by aparticular array location. The set of anatomical location pointscomprises the domain of the image. In 2-D digital images, or slicesections, the discrete array locations are termed pixels.Three-dimensional digital images can be constructed from stacked slicesections through various construction techniques known in the art. The3-D images are made up of discrete volume elements, also referred to asvoxels, composed of pixels from the 2-D images. The pixel or voxelproperties can be processed to ascertain various properties about theanatomy of a patient associated with such pixels or voxels.

The process of classifying, identifying, and characterizing imagestructures is known as segmentation. Once anatomical regions andstructures are identified by analyzing pixels and/or voxels, subsequentprocessing and analysis exploiting regional characteristics and featurescan be applied to relevant areas, thus improving both accuracy andefficiency of the imaging system. One method for characterizing shapesand segmenting objects is based on tobogganing. Tobogganing is anon-iterative, single-parameter, linear execution time over-segmentationmethod. It is non-iterative in that it processes each image pixel/voxelonly once, thus accounting for the linear execution time. The sole inputis an image's ‘discontinuity’ or ‘local contrast’ measure, which is usedto determine a slide direction at each pixel. One implementation oftobogganing uses a toboggan potential for determining a slide directionat each pixel/voxel. The toboggan potential is computed from theoriginal image, in 2D, 3D or higher dimensions, and the specificpotential depends on the application and the objects to be segmented.One simple, exemplary technique for defining a toboggan potential wouldbe as the intensity difference between a given pixel and its nearestneighbors. Each pixel is then ‘slid’ in a direction determined by amaximum (or minimum) potential. All pixels/voxels that slide to the samelocation are grouped together, thus partitioning the image volume into acollection of voxel clusters. Tobogganing can be applied to manydifferent anatomical structures and different types of data sets, e.g.CT, MR, PET etc., on which a toboggan type potential can be computed.

SUMMARY OF THE INVENTION

Exemplary embodiments of the invention as described herein generallyinclude methods and systems for a toboggan-based shape characterizationand object segmentation that includes computing a toboggan potential,tobogganing, extracting object of interest and computing shape featureparameters. In the approaches herein described, a pixel or voxel slidesonly when necessary, and the toboggan potential is computed only whenneeded in the toboggan process. Toboggan processes according toembodiments of the invention are accelerated as compared to currenttoboggan processes due to a more efficient computation and the selectionof the locus in which the computation is performed.

According to an aspect of the invention, there is provided a method foridentifying an object in an image, including providing a digitized imagecomprising a plurality of intensities corresponding to a domain ofpoints in a N-dimensional space, finding a point in the image that is aconcentration location, expanding from said concentration point byincluding neighboring points of said concentration point based on atoboggan potential of each neighboring point to form a cluster ofpoints, and obtaining an object from said cluster.

According to a further aspect of the invention, expanding from saidconcentration point further comprises marking said concentrationlocation with a unique label, marking the neighboring points of theconcentration location with said unique label, selecting a marked pointwith an extremal toboggan potential value, identifying those neighborsof said selected point that slide to the selected point, marking thoseneighbors that slide to the selected point that are unmarked with theselected point's label, and adding the selected point to said cluster ofpoints.

According to a further aspect of the invention, selecting a point withan extremal toboggan potential value comprises computing a tobogganpotential for each said marked point.

According to a further aspect of the invention, identifying thoseneighbors that slide to the selected point comprises determining a slidedirection for all neighbors of said selected point.

According to a further aspect of the invention, the steps of selecting apoint with an extremal potential value, identifying neighbors, markingneighbors, and adding the selected point to the cluster are repeateduntil there are no more marked points.

According to a further aspect of the invention, the extremal potentialis a minimum potential.

According to a further aspect of the invention, the extremal potentialis a maximum potential.

According to a further aspect of the invention, finding a point in theimage that is a concentration location further comprises, selecting apoint in the image, finding a neighboring point with an extremalpotential with respect to the selected point, sliding to saidneighboring point, and repeating the steps of finding a neighboringpoint with an extremal potential and sliding to said neighboring pointuntil a point is reached that cannot slide to a neighbor point.

According to a further aspect of the invention, finding a neighboringpoint with an extremal potential comprises determining the potential ofeach neighbor of the selected point.

According to a further aspect of the invention, the extremal potentialis a minimum potential.

According to a further aspect of the invention, the extremal potentialis a maximum potential.

According to another aspect of the invention, there is provided aprogram storage device readable by a computer, tangibly embodying aprogram of instructions executable by the computer to perform the methodsteps for identifying an object in a digital image.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a 2D artificial image created to resemble a colon crosssection, according to an embodiment of the invention.

FIG. 2 depicts a distance map computed from FIG. 1, and how pixels inthe object of interest were slid to their respective concentrationpoints, according to an embodiment of the invention.

FIG. 3 depicts a cluster determined by dynamic fast tobogganing,according to an embodiment of the invention.

FIG. 4 depicts a flow chart of a dynamic fast toboggan method, accordingto an embodiment of the invention.

FIG. 5 depicts a flow chart of a toboggan cluster merger, according toan embodiment of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Exemplary embodiments of the invention as described herein generallyinclude systems and methods for performing a toboggan-based objectsegmentation using a distance transform to find and characterize shapesin digital medical images. Although an exemplary embodiment of thisinvention is discussed in the context of segmenting and characterizingthe colon and in particular colon polyps, it is to be understood thatthe toboggan-based object segmentation methods presented herein haveapplication to 3D CT images, and to images from different modalities ofany dimensions on which a gradient field can be computed and toboggancan be performed. For simplicity of discussion, the embodimentspresented herein are presented in terms of a 2D artificial-image. It isto be understood that this 2D artificial-image is exemplary andnon-limiting, and that the methods herein disclosed are applicable tosegmenting and identifying objects in digital images of arbitrary. Inparticular, although reference is made to pixels, it is to be understoodthat in the context of a 3D or higher dimensional images, the term‘pixel’ can be replaced by the term ‘voxel’.

In tobogganing, each pixel in an object of interest slides to a neighborwith a minimal potential or climbs to a neighbor with a maximalpotential. This process of sliding/climbing is referred to atobogganing. The tobogganing terminates at a pixel that is either alocal minimum or a local maximum. This terminating pixel is referred toas a concentration location. All the pixels that slide/climb togetherform a toboggan-cluster.

Tobogganing relies on a computed potential to determine the slidingdirection at each location (voxel or pixel). There are many options inselecting toboggan potential. One exemplary, non-limiting potential canbe obtained from a distance map resulting from the computation of adistance transform, disclosed in the inventor's co-pending application,“System and Method for Toboggan-based Object Segmentation using DistanceTransform”, U.S. patent application Ser. No. 10/______, filedconcurrently herewith. In order to determine a distance map, anintensity threshold is determined for the pixels in an image, wherepoints with an intensity above a pre-determined intensity threshold formthe object of interest, while those whose intensity is below thethreshold value form a reference object. For example, FIG. 1 presents a2D artificial-image created to resemble colon cross-section, with theobject of interest being a polyp, defined by tissue values greater than500 in this example, surrounded by the reference object, the lumen,defined in this example by tissue values below 500. A distance map canbe computed for each pixel in the object of interest, where the distancemap is defined as the distance from the pixel to a pixel in thereference object. FIG. 2 depicts the distance map computed from FIG. 1,and how pixels in the object of interest were slid to their respectiveconcentration points. Pixels represented by non-zero values form theobject of interest, while pixels represented by zeros form the referenceobject. The pixel values are the distance transform potential values foreach pixel. The sliding direction of the pixels in the object ofinterest are indicated by the arrows in the figure. The concentrationlocations are circled. In this example, 16 toboggan clusters wereformed, of which 11 are single-pixel clusters. No tobogganing isperformed on pixels with zero potential.

However, the computational efficiency and resource usage can be improvedupon by performing the toboggan computation only on those pixels ofinterest, and by computing the toboggan potential only as portion of anexpansion from the concentration location, an acceleration referred toherein as fast tobogganing. Therefore, a dynamic toboggan potential isintroduced that only computes the potential for a specified location. Inthe example presented above, the potential is the distance transform.For a given pixel, fast tobogganing forms a toboggan cluster thatcontains the given pixel without scanning the whole image. For example,if the concentration location in the image is the given pixel, then thedesired toboggan cluster is that which contains the concentrationlocation, depicted as being circled in FIG. 3. The cluster can be foundsliding outward for the concentration location. Thus, one first searchesfor a concentration point and then expands a cluster from it, ratherthan tobogganing every point to a concentration location and thenselecting the cluster that contains a given location.

FIG. 4 depicts a flow chart of a dynamic fast tobogganing methodaccording to an embodiment of the invention. At step 41, the tobogganconcentration location is found. A selected location, either provided bya user or automatically generated, is regarded as a current voxel and isslid/climbed to a neighbor with an extremal potential. The extrema canbe either a maximum or a minimum, depending upon the application. Theprocess is repeated, with each neighbor so reached being regarded as thecurrent voxel and being slid/climbed it until a concentration location,i.e. a voxel that cannot slide/climb to any of its neighbors, isreached. In the example depicted in FIG. 2, the center point, whosedistance map value is 1.0, climbs to neighboring pixels with a maximumpotential. These pixels have potential values of, successively, 1.4,2.0, 2.2, and finally 2.8, which is a circled concentration location,labeled ‘C’. Note that the concentration location is a local maximum:there are no pixels surrounding the concentration point with a potentialgreater that that of the concentration location. If the starting pixelis already a concentration point, it cannot slide, and then theprocessing can proceed to the next step.

The example depicted in FIG. 2 showed a pixel sliding to a neighbor witha maximum potential. Alternatively, an application could require that apixel slide to a neighbor with a minimum potential. In this case, theconcentration location would be a pixel with a local minimum potential,and no neighbor would have a potential less than that of theconcentration location.

The next step is to expand from the concentration location to form atoboggan cluster. This could be done in a number of ways. According tothe exemplary embodiments of the invention presented herein, theexpansion can utilize two data structures. One is a cluster-member list,which can include all the pixels assigned to the cluster. The other datastructure is an active-pixels list, which includes all the neighbors ofthose pixels in the cluster-member list. The active-pixel list can beimplemented in any manner that permits a quick search, such as apriority queue or an open list, so that a pixel with a maximal/minimalpotential can be found quickly for inclusion.

The expansion process can be described as a base and an iterative step.In a base step of the expansion, step 42, the concentration location istaken as the current expanded voxel, and is assigned a unique tobogganlabel. The cluster-member list is initialized with the concentrationlocation. Its neighbors are marked and pushed onto the active pixelslist. Marking the neighbors helps to ensure the uniqueness of a voxel inthe active-pixels list.

The next steps are the series of repeated steps. First, at step 43, thetoboggan potential is computed for each added neighbor in theactive-pixels list. From the active-pixels list, a voxel with theminimal/maximal potential with respect to the current expanded voxel isselected and popped from the active-pixels list. This popped voxelbecomes the current expanded voxel. At step 44, the sliding directionsof the current expanded voxel are determined and those neighboringvoxels to which it slides are identified and, if unmarked, are labeledwith the label of the current expanded voxel. At step 45, the previouslyunmarked neighbors are added to the active-pixels list, and the currentexpanded voxel is added to the appropriate cluster-member list asdetermined by its concentration location label. If, at step 46, theactive-pixels list is not empty, the previous steps 43, 44, 45 arerepeated for each voxel in the active-pixels list with a extremalpotential with respect to the current expanded voxel. Upon finishing,the cluster-member list includes 47 all pixels in the cluster. Thesliding direction for each pixel in the cluster-member list can also berecorded during the tobogganing process.

In a fast dynamic tobogganing according to an embodiment of theinvention, only a small number of pixels, i.e. the pixels in thetoboggan cluster containing the click point and those pixels on theboundary of the toboggan cluster, are involved. FIG. 3 depicts a clusterdetermined by dynamic fast tobogganing. The cluster being formed iscentered on the lower edge of the image, its concentration location ‘C’being at the center of the lower edge with potential 2.8. Note thearrows indicating how pixels in the cluster slide to the concentrationlocation. In the example depicted in FIG. 3, pixels in the clusterconcentrated around pixel ‘C’ are visited, since they are included inthe toboggan cluster containing the click point ‘P’. Therefore, oneneeds only to compute the potential for those pixels. The pixels markedwith an ‘S’ are surface pixels which border pixels in the referenceregion (those with potential 0.0). In addition to the cluster memberpixels, those pixels marked with ‘V’ participate in the dynamic fasttobogganing process. Those pixels marked with ‘X’ do not participate inthe determination of this cluster.

A dynamic fast tobogganing according to an embodiment of the inventioncomputes the potential of a pixel only when the pixel is pushed to theactive-pixels list. No distance is computed for any of those pixelsmarked with an ‘X’ in FIG. 3, as those pixels are never pushed onto anactive-pixels list for the concentration point ‘C’. There is nolimitation on the toboggan potentials useful with a dynamic fasttoboggan process according to an embodiment of the invention. Forexample, a potential can be globally defined, by convolving the selectedregion of interest with a normalized gradient field centered at acurrent expanded voxel. Alternatively, a distance potential for a voxelcan be defined locally by, for example, determining a distance from thevoxel to a nearest voxel in a reference region. The dynamic distancetransform, disclosed in the inventors' copending application “System andMethod for Toboggan-based Object Segmentation using Distance Transform”,is useful for this purpose, as only when a pixel is pushed onto theactive-pixels list is its distance computed.

Simulations performed on a 43-cubed sub-volume, based on a specifiedlocation, indicate that a dynamic fast toboggan method according to anembodiment of the invention can be as much as ten times faster thanprevious toboggan methods.

It is to be understood that the present invention can be implemented invarious forms of hardware, software, firmware, special purposeprocesses, or a combination thereof. In one embodiment, the presentinvention can be implemented in software as an application programtangible embodied on a computer readable program storage device. Theapplication program can be uploaded to, and executed by, a machinecomprising any suitable architecture.

Referring now to FIG. 5, according to an embodiment of the presentinvention, a computer system 51 for implementing the present inventioncan comprise, inter alia, a central processing unit (CPU) 52, a memory53 and an input/output (I/O) interface 54. The computer system 51 isgenerally coupled through the I/O interface 54 to a display 55 andvarious input devices 56 such as a mouse and a keyboard. The supportcircuits can include circuits such as cache, power supplies, clockcircuits, and a communication bus. The memory 53 can include randomaccess memory (RAM), read only memory (ROM), disk drive, tape drive,etc., or a combinations thereof. The present invention can beimplemented as a routine 57 that is stored in memory 53 and executed bythe CPU 52 to process the signal from the signal source 58. As such, thecomputer system 51 is a general purpose computer system that becomes aspecific purpose computer system when executing the routine 57 of thepresent invention.

The computer system 51 also includes an operating system and microinstruction code. The various processes and functions described hereincan either be part of the micro instruction code or part of theapplication program (or combination thereof) which is executed via theoperating system. In addition, various other peripheral devices can beconnected to the computer platform such as an additional data storagedevice and a printing device.

It is to be further understood that, because some of the constituentsystem components and method steps depicted in the accompanying figurescan be implemented in software, the actual connections between thesystems components (or the process steps) may differ depending upon themanner in which the present invention is programmed. Given the teachingsof the present invention provided herein, one of ordinary skill in therelated art will be able to contemplate these and similarimplementations or configurations of the present invention.

The particular embodiments disclosed above are illustrative only, as theinvention may be modified and practiced in different but equivalentmanners apparent to those skilled in the art having the benefit of theteachings herein. Furthermore, no limitations are intended to thedetails of construction or design herein shown, other than as describedin the claims below. It is therefore evident that the particularembodiments disclosed above may be altered or modified and all suchvariations are considered within the scope and spirit of the invention.Accordingly, the protection sought herein is as set forth in the claimsbelow.

1. A method of identifying an object in an image comprising the stepsof: providing a digitized image comprising a plurality of intensitiescorresponding to a domain of points in a N-dimensional space; finding apoint in the image that is a concentration location; expanding from saidconcentration point by including neighboring points of saidconcentration point based on a toboggan potential of each neighboringpoint to form a cluster of points; and obtaining an object from saidcluster.
 2. The method of claim 1, wherein expanding from saidconcentration point further comprises: marking said concentrationlocation with a unique label; marking the neighboring points of theconcentration location with said unique label; selecting a marked pointwith an extremal toboggan potential value; identifying those neighborsof said selected point that slide to the selected point; marking thoseneighbors that slide to the selected point that are unmarked with theselected point's label; and adding the selected point to said cluster ofpoints.
 3. The method of claim 2, wherein selecting a point with anextremal toboggan potential value comprises computing a tobogganpotential for each said marked point.
 4. The method of claim 2, whereinidentifying those neighbors that slide to the selected point comprisesdetermining a slide direction for all neighbors of said selected point.5. The method of claim 2, wherein the steps of selecting a point with anextremal potential value, identifying neighbors, marking neighbors, andadding the selected point to the cluster are repeated until there are nomore marked points.
 6. The method of claim 2, wherein the extremalpotential is a minimum potential.
 7. The method of claim 2, wherein theextremal potential is a maximum potential.
 8. The method of claim 1,wherein finding a point in the image that is a concentration locationfurther comprises: selecting a point in the image; finding a neighboringpoint with an extremal potential with respect to the selected point;sliding to said neighboring point; and repeating the steps of finding aneighboring point with an extremal potential and sliding to saidneighboring point until a point is reached that cannot slide to aneighbor point.
 9. The method of claim 8, wherein finding a neighboringpoint with an extremal potential comprises determining the potential ofeach neighbor of the selected point.
 10. The method of claim 9, whereinthe extremal potential is a minimum potential.
 11. The method of claim9, wherein the extremal potential is a maximum potential.
 12. A methodof identifying an object in a digital image, comprising the steps of:providing a digital image comprising a plurality of intensitiescorresponding to a domain of points in a N-dimensional space; finding apoint in the image that is a concentration location; initializing acluster with said concentration location; adding the neighboring pointsof the concentration location to a list; selecting a neighbor point withan extremal potential value from said list; determining a slidedirection of all neighbors of said selected point and identifying thoseneighbors that slide to the selected point; adding those neighbor pointsnot already in the list to the list; adding the selected point to thecluster; and repeating the steps of selecting a neighbor point with anextremal potential value, determining a slide direction, adding pointsto the list, and adding the selected point to the cluster, until thelist is empty.
 13. The method of claim 12, further comprisingidentifying an object from said cluster.
 14. The method of claim 12,further comprising marking said concentration location with a label. 15.The method of claim 14, further comprising marking the neighbors of saidconcentration location with said label.
 16. The method of claim 15,further comprising marking those neighbors that slide to the selectedpoint and that are unmarked with the selected point's label.
 17. Themethod of claim 12, further comprising determining a toboggan potentialfor each neighbor of said concentration location.
 18. The method ofclaim 17, wherein said toboggan potential is based on a distance map ofeach neighbor to a reference object.
 19. A program storage devicereadable by a computer, tangibly embodying a program of instructionsexecutable by the computer to perform the method steps for identifyingan object in an image, said method comprising the steps of: providing adigitized image comprising a plurality of intensities corresponding to adomain of points in a N-dimensional space; finding a point in the imagethat is a concentration location; expanding from said concentrationpoint by including neighboring points of said concentration point basedon a toboggan potential of each neighboring point to form a cluster ofpoints; and obtaining an object from said cluster.
 20. The computerreadable program storage device of claim 19, wherein expanding from saidconcentration point further comprises: marking said concentrationlocation with a unique label; marking the neighboring points of theconcentration location with said unique label; selecting a marked pointwith an extremal toboggan potential value; identifying those neighborsof said selected point that slide to the selected point; marking thoseneighbors that slide to the selected point that are unmarked with theselected point's label; and adding the selected point to said cluster ofpoints.
 21. The computer readable program storage device of claim 20,wherein selecting a point with an extremal toboggan potential valuecomprises computing a toboggan potential for each said marked point. 22.The computer readable program storage device of claim 20, whereinidentifying those neighbors that slide to the selected point comprisesdetermining a slide direction for all neighbors of said selected point.23. The computer readable program storage device of claim 20, whereinthe steps of selecting a point with an extremal potential value,identifying neighbors, marking neighbors, and adding the selected pointto the cluster are repeated until there are no more marked points. 24.The computer readable program storage device of claim 20, wherein theextremal potential is a minimum potential.
 25. The computer readableprogram storage device of claim 20, wherein the extremal potential is amaximum potential.
 26. The computer readable program storage device ofclaim 19, wherein finding a point in the image that is a concentrationlocation further comprises: selecting a point in the image; finding aneighboring point with an extremal potential with respect to theselected point; sliding to said neighboring point; and repeating thesteps of finding a neighboring point with an extremal potential andsliding to said neighboring point until a point is reached that cannotslide to a neighbor point.
 27. The computer readable program storagedevice of claim 26, wherein finding a neighboring point with an extremalpotential comprises determining the potential of each neighbor of theselected point.
 28. The computer readable program storage device ofclaim 27, wherein the extremal potential is a minimum potential.
 29. Thecomputer readable program storage device of claim 27, wherein theextremal potential is a maximum potential.